Preheat oven to 170 C/ 160 C (fan)/ gas mark 3 and grease and line a 6 inch deep cake tin with a round of baking paper.
Over a low heat melt the butter and olive oil together and set aside to cool while you prepare the rest of the ingredients.
Blitz your pistachio nuts in a high speed blender until fine and add the coconut, flour, baking powder and salt. Blitz for another second or two.
In a medium sized bowl whisk the eggs with the granulated sugar until the mixture is light and fluffy and forms ribbons when you lift the whisk up. This will take a few minutes if you're using arm power.
Add the melted butter to the eggs along with the yogurt and stir until combined.
Fold in the nut mixture until well incorporated and spoon into the prepared tin.
Bake for 45-50 minutes until light golden. A wooden skewer inserted into the centre of the cake will come out clean when it is finished.
While the cake is still warm use the wooden skewer to poke holes evenly around the top.
Dissolve the rose syrup or jam in a bit of hot water, if needed, and spoon over the top of the cake. Press half of the chopped pistachios and coconut flakes into the top of the cake while the jam is still sticky, so some of it sticks to the top.
Leave the cake to cool in the tin for at least 15 minutes before transferring to a wire rack to cool completely.
Sprinkle the remaining topping and the rose petals over the cake and serve with a cup of afternoon tea.
Mum of three, daydream adventurer, OU Life Sciences graduate, occasional crafter, ex-pat Canadian & quite possibly Britain's most northerly food blogger.